Improved FTA Methodology and Application to Subsea Pipeline Reliability Design

<div><p>An innovative logic tree, Failure Expansion Tree (FET), is proposed in this paper, which improves on traditional Fault Tree Analysis (FTA). It describes a different thinking approach for risk factor identification and reliability risk assessment. By providing a more comprehensive and objective methodology, the rather subjective nature of FTA node discovery is significantly reduced and the resulting mathematical calculations for quantitative analysis are greatly simplified. Applied to the Useful Life phase of a subsea pipeline engineering project, the approach provides a more structured analysis by constructing a tree following the laws of physics and geometry. Resulting improvements are summarized in comparison table form.</p></div

Demonstration of calculated results from two different tree structures with interchanged layers.

<p>On top of each box, the number is the proposed percent allocation with respect to the box above it. Node probability is the product of all layers above it and is calculated on the right hand side for Debris impact and Valve failures.</p

A typical Fault Tree analysis.

<p>This example for a Subsea Pipeline System is taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093042#pone.0093042-Xie1" target="_blank">[3]</a>.</p

Process Flow Diagram for development of a FTA.

<p>Process Flow Diagram for development of a FTA.</p

Rank Order Analysis of Useful Life factors.

<p>Calculations for ranking are based on the organization of the FET in Fig. 3. Under Source Reference Codes, values are from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093042#pone.0093042-Xie3" target="_blank">[23]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093042#pone.0093042.s003" target="_blank">Table S3</a>. Letters and “?” were not identified or evaluated by the original FTA, so corresponding probability data are unavailable. For demonstration purposes only, missing items are arbitrarily divided equally based on the number of nodes within a given level and“?” are denoted as “0”. Obviously, proper values should be inserted by field experts or suitably researched.</p

Failure Expansion Tree for identifying the risk factors in a subsea pipeline system during Useful life.

<p>Boxes crossed off with a dashed line would be considered in other branches of a complete FET. Failure codes on top of the boxes refer to nodes taken from Reference <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093042#pone.0093042-Xie1" target="_blank">[3]</a> (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093042#pone.0093042.s002" target="_blank">Table S2</a>) and are shown for comparison purposes only. Figures to the right of the boxes refer to probability data taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093042#pone.0093042-Xie3" target="_blank">[23]</a> and used in the rank order analysis of Fig. 4. Question marks are failure modes unidentified in the original FTA analysis. We call these reliability design “leakage”; they are areas where rare events, being unforeseen, might occur.</p

Energy Function Model (EFM) for piping in a subsea pipeline system.

<p>The Function Flow Model of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103937#pone-0103937-g004" target="_blank">Fig. 4</a> expanded to include system energies. Cells with Bold font are direct energy side effects associated with the designed functions or other cells immediate above/below. Bolded cells are fed forward into the MEOST experiment using the energy codes to the right of each bolded box.</p

Energy Expansion Tree as applied to piping in a subsea pipeline.

<p>Boxes with bold font represent the energies to be fed into MEOST. Boxes with various shaded backgrounds and borders are used to distinguish the corresponding branch development underneath it. Numbers to the right of bolded boxes are used for linking the energies into the subsequent MEOST table.</p

High-level Function Flow Model (FFM) for a subsea pipeline system.

<p>The function model shows three primary functions required to deliver oil inland. Each box states a function (a verb) and boxes to its right explain HOW that function is achieved. Vertical linkages (the WHEN direction) show consequences of functions.</p

Genetic variants of PTGS2, TXA2R and TXAS1 are associated with carotid plaque vulnerability, platelet activation and TXA2 levels in ischemic stroke patients

<div><p>Eicosanoids may play a role in ischemic stroke. However, the associations of variants in cyclooxygenase (COX) pathway genes and interaction among these variants with carotid plaque vulnerability are not fully understood. In present study, twelve variants in COX pathway genes were examined using matrix-assisted laser desorption ionization time-of-flight mass spectrometry method in 396 patients with ischemic stroke and 291 controls. Platelet aggregation, platelet-leukocyte aggregates, and urine 11-dehydrothromboxane B2 (11-dTxB2) were also measured. According to the results of carotid high-resolution B-mode ultrasound, the patients were stratified into the following groups [i.e., non-carotid plaque and carotid plaque. The carotid plaque was further classified into subgroups of echolucent plaque (ELP) and echogenic plaque (EGP)]. Additionally, gene-gene interactions were analyzed to assess whether there was any interactive role for assessed variants in affecting carotid plaque vulnerability, platelet activation and 11-dTxB2 levels. There were no significant differences in the frequencies of genotypes of the twelve variants between patients and controls. Among 396 patients, 294 cases (74.2%) had carotid plaques (106 had ELP, 188 had EGP). Frequency of <i>PTGS2</i> rs20417CC, <i>TXAS1</i> rs2267679TT, <i>TXAS1</i> rs41708TT, <i>PTGIS</i> rs5602CC, and <i>TXA2R</i> rs1131882TT genotype was significantly higher in patients with plaque compared with patients without plaque, or in patients with ELP compared with patients with EGP. 11-dTxB₂ levels, platelet aggregation and platelet-leukocyte aggregates were significantly higher in patients with ELP compared with patients without plaque or with EGP. Multivariate logistic regression analysis revealed that <i>PTGS2</i> rs20417CC, <i>TXA2R</i> rs1131882TT, and high-risk interaction among variants in <i>PTGS2</i> rs20417, <i>TXA2R</i> rs1131882 and <i>TXAS1</i> rs41708 were independently associated with the risk of ELP after adjusting for confounding variables. The variants in COX pathway genes and the high-risk interactions among variants in <i>PTGS2</i> rs20417, <i>TXA2R</i> rs1131882 and <i>TXAS1</i> rs41708 were associated with high 11-dTxB2 and platelet activation, and independently associated with the risk of carotid plaque vulnerability. These variants might be potential markers for plaque instability.</p></div